# Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids

## TL;DR

This paper models and analyzes the radial oscillations of small bubbles in yield-stress fluids under acoustic pressure, revealing how yielding influences bubble dynamics and identifying conditions for bubble release.

## Contribution

It introduces a novel numerical approach using EVP constitutive equations to study bubble oscillations and yields in complex fluids, providing analytical and simulation insights.

## Key findings

- Critical acoustic pressure for yielding is identified.
- Bubble oscillation amplitude varies with applied pressure.
- Yielding impacts bubble dynamics significantly.

## Abstract

We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluid and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elasto-visco-plastic (EVP) constitutive equation that takes into account the elastic and visco-plastic deformations of the material [P. Saramito, J. NonNewton. Fluid Mech. 158 (1-3) (2009) pp.154-161]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ODEs and an integrodifferential equation, which we solve numerically for the case of two yield-stress fluids, a sot Carbopol gel and a stiffer Kaolin suspension. We find that, depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material. We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including oil industry and food processing.